I was asked a two part question, first prove the AM-GM inequality for n=2 (with some extra)
$\frac{2}{\frac{1}{a}+\frac{1}{b}}\leq\sqrt{ab}\leq\frac{a+b}{2}$
I was able to do that without too many problems.

Then I'm asked to deduce from the above that
$\frac{4}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}}\leq\sqrt[4]{abcd}\leq\frac{a+b+c+d}{4}$
I think it just have something to do with applying the inequity proven earlier a few times, it just feels like a trick question where I'm missing something.
Any ideas?